Discussiones Mathematicae Graph Theory 27(3) (2007) 409-423
doi: 10.7151/dmgt.1371

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EFFICIENT (j,k)-DOMINATION

ROBERT R. RUBALCABA1  AND  PETER J. SLATER1,2

1Department of Mathematical Sciences
University of Alabama in Huntsville
Huntsville, AL 35899, USA
e-mail: r.rubalcaba@gmail.com

2Department of Computer Science
University of Alabama in Huntsville
Huntsville, AL 35899, USA
e-mail: slater@math.uah.edu

Abstract

A dominating set S of a graph G is called efficient if |N[v]∩ S| = 1 for every vertex v ∈ V(G). That is, a dominating set S is efficient if and only if every vertex is dominated exactly once. In this paper, we investigate efficient multiple domination. There are several types of multiple domination defined in the literature: k-tuple domination, {k}-domination, and k-domination. We investigate efficient versions of the first two as well as a new type of multiple domination.

Keywords: efficient domination, multiple domination.

2000 Mathematics Subject Classification: 05C69.

References

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Received 1 April 2006
Revised 16 May 2007
Accepted 16 May 2006